Find the derivative of the functions

Question

Find the derivative of the functions f(x)=x^2+2x-1 and g(x)=1/2x^3-4x+1.

Answer 1

f'(x)= 2x+2

g'(x)= (3/2)x^2 - 4 (assuming you meant (1/2)x^3 and not 1/(2x^3))

general rule: take the exponent and make it a coefficient, then reduce the exponent by 1

derivative of x^2 becomes 2x^(2-1) = 2x^1 = 2x

another rule: derivative of a sum =sum of the derivatives

Answer 2

Both are done using the Power Rule. Do you have a question about that?